Chapter 2.3, Problem 46E

CRIMINAL JUSTICE The body of Alisha was discovered in the basement of the company where she worked. The medical examiner determined that she was killed between $9$ P.M. and $10$ P.M. After a preliminary investigation, homicide detectives decided to question three of her coworkers: Alex, Bob, and Charlie. The detectives were told by the suspects that Alex left work at $9:18$ P.M. on the day of the homicide, walked $1000\text{ft}$ to his car, and drove $16\text{mi}$ to his house, arriving home at $9:40$ P.M. Bob left work at $9:12$ P.M., walked $400\text{ft}$ to his car, and drove $12\text{mi}$ to his house, arriving home at $9:30$ P.M. Charlie punched out at $9:35:30$ P.M., walked $600\text{ft}$ to his car, and drove $20\text{mi}$ to his house, arriving home at $10$ P.M. After analyzing this information, the detectives singled out Bob for further questioning. Explain why. Hint: Suppose that each man walks at an average speed of $\text{n}\text{ft}/\sec$ and drives his car at an average speed of $w\text{ft}/\sec$.

(i) Show that this leads to the equations

$\frac{1000}{n}+\frac{84,480}{w}=1320$	$\frac{400}{n}+\frac{63,360}{w}=1080$
$\frac{600}{n}+\frac{105,600}{w}=1470$

(ii) Show that these equations can be expressed in the form

$1000x+84,480y=1320$	$400x+63,360y=1080$
$600x+105,600y=1470$

Then solve each possible pair of equations in System (ii).